scholarly journals Positive Solutions for (k,n−k) Conjugate Multipoint Boundary Value Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yulin Zhao
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Real Banach Space ◽  
Boundary Value ◽  
Index Theory ◽  
Zero Element ◽  
Singular Boundary ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problems

By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem(-1)n-kun(t)=f(t,ut),0<t<1,n≥2,1≤k≤n-1,u(0)=∑i=1m-2‍aiu(ξi),u(i)(0)=u(j)(1)=θ,1≤i≤k−1,0≤j≤n−k−1in a real Banach spaceE, whereθis the zero element ofE,0<ξ1<ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2.As an application, we give two examples to demonstrate our results.

scholarly journals Positive solutions of singular nonlinear Sturm-Liouville boundary value problems

2004 ◽  
Vol 45 (4) ◽  
pp. 557-571
Author(s):  
Yan Sun ◽  
Lishan Liu ◽  
Yeol Je Cho
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractBy using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.

scholarly journals Existence, Nonexistence and Multiplicity of Positive Solutions for Singular Boundary Value Problems Involving φ-Laplacian

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 953 ◽  
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Interesting Point ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving φ -Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.

Existence, multiplicity and non-existence of positive solutions for two-point boundary-value problems with strong singularity

2010 ◽  
Vol 140 (6) ◽  
pp. 1187-1196
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Image Position

We study the existence, multiplicity and non-existence of positive solutions for the singular two-point boundary-value problemswhere $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$, λ is a non-negative real parameter and f ∈ C((0, 1) × [0,∞), (0,∞)). Here, f(t, u) may be singular at t = 0 and/or 1. To obtain the main results we use the global continuation theorem and fixed-point index theory.

scholarly journals Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yongxiang Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Index Theory ◽  
Periodic Boundary Value Problem ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1),  i=0,1,2,3, wheref:[0,1]×R+×R→R+is continuous,α,β∈R,and satisfy0<α<((β/2)+2π2)2,β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.

Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

2020 ◽  
Vol 24 (1) ◽  
pp. 109-129
Author(s):  
Abdulkadir Dogan ◽  
John R. Graef
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Third Order ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

scholarly journals Positive Solutions for a Class of Fourth-Orderp-Laplacian Boundary Value Problem Involving Integral Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yan Sun
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Integral Boundary Conditions ◽  
Index Theory ◽  
Integral Conditions ◽  
Interesting Point ◽  
Integral Boundary ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions forp-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples to demonstrate the main results.

scholarly journals Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jingjing Cai ◽  
Guilong Liu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence And Nonexistence

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

scholarly journals Application of Fixed-Point Index Theory for a Nonlinear Fractional Boundary Value Problem with an Advanced Argument

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Li Wu ◽  
Chuanzhi Bai
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Fractional Boundary Value Problem ◽  
Point Index ◽  
Advanced Argument ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, we investigate the existence of positive solutions of a class of fractional three-point boundary value problem with an advanced argument by using fixed-point index theory. Our results improve and extend some known results in the literature. Two examples are given to demonstrate the effectiveness of our results.

scholarly journals Positive Solutions for a System of Fourth-Order p-Laplacian Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Lianlong Sun ◽  
Zhilin Yang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Index Theory ◽  
Priori Estimates ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

We investigate the existence of positive solutions for the system of fourth-order p-Laplacian boundary value problems (|u′′|p-1u′′)′′=f1(t,u,v),  (|v′′|q-1v′′)′′=f2(t,u,v),  u(2i)(0)=u(2i)(1)=0,  i=0,1,  v(2i)(0)=v(2i)(1)=0,  i=0,1, where p,q>0 and f1,f2∈C([0,1]×ℝ+2,ℝ+)  (ℝ+:=[0,∞)). Based on a priori estimates achieved by utilizing Jensen’s integral inequalities and nonnegative matrices, we use fixed point index theory to establish our main results.

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